{"doi":"10.1057/s41599-021-00903-w","title":"Growth rates of modern science: a latent piecewise growth curve approach to model publication numbers from established and new literature databases","abstract":"<jats:title>Abstract</jats:title><jats:p>Growth of science is a prevalent issue in science of science studies. In recent years, two new bibliographic databases have been introduced, which can be used to study growth processes in science from centuries back: Dimensions from Digital Science and Microsoft Academic. In this study, we used publication data from these new databases and added publication data from two established databases (Web of Science from Clarivate Analytics and Scopus from Elsevier) to investigate scientific growth processes from the beginning of the modern science system until today. We estimated regression models that included simultaneously the publication counts from the four databases. The results of the unrestricted growth of science calculations show that the overall growth rate amounts to 4.10% with a doubling time of 17.3 years. As the comparison of various segmented regression models in the current study revealed, models with four or five segments fit the publication data best. We demonstrated that these segments with different growth rates can be interpreted very well, since they are related to either phases of economic (e.g., industrialization) and/or political developments (e.g., Second World War). In this study, we additionally analyzed scientific growth in two broad fields (Physical and Technical Sciences as well as Life Sciences) and the relationship of scientific and economic growth in UK. The comparison between the two fields revealed only slight differences. The comparison of the British economic and scientific growth rates showed that the economic growth rate is slightly lower than the scientific growth rate.</jats:p>","journal":"Humanities and Social Sciences Communications","year":2021,"id":9897,"datarank":1.4651389846905176,"base_score":3.713572066704308,"endowment":3.713572066704308,"self_citation_contribution":0.5570358100056463,"citation_network_contribution":0.9081031746848713,"self_endowment_contribution":0.5570358100056463,"citer_contribution":0.9081031746848713,"corpus_percentile":61.92026037428804,"corpus_rank":469,"citation_count":334,"citer_count":39,"citers_with_citation_signal":26,"citers_with_endowment":26,"datacite_reuse_total":0,"is_dataset":true,"is_dataset_confidence":0.8156,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-10-07","fair_score":30.2083,"fair_percentile":12.335092348284961,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":839,"name":"Robin Haunschild","orcid":"0000-0001-7025-7256","position":1,"is_corresponding":false},{"id":12196,"name":"Rüdiger Mutz","orcid":"0000-0003-3345-6090","position":2,"is_corresponding":false},{"id":6190,"name":"Ruediger Mutz","orcid":null,"position":3,"is_corresponding":false},{"id":661,"name":"Lutz Bornmann","orcid":"0000-0003-0810-7091","position":0,"is_corresponding":true}],"reference_count":55,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":"gold","license":"cc-by","views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":20.0,"fair_a":55.0,"fair_i":12.5,"fair_r":33.3333,"fair_zscore":-1.3571,"fair_rationale":{"fair_score":30.21,"has_llm":true,"dimensions":{"F":{"name":"Findable","score":20.0,"criteria":[{"key":"f_has_doi","label":"Has a persistent DOI","kind":"deterministic","weight":1.0,"fraction":1.0,"signal":"DOI present","rationale":null},{"key":"f_repository_presence","label":"Indexed in repositories / literature DBs","kind":"deterministic","weight":1.0,"fraction":0.0,"signal":"datacite=0, pmcid=False, pmid=False","rationale":null},{"key":"f_persistent_ids","label":"Resolvable scholarly identifiers (OpenAlex)","kind":"deterministic","weight":0.5,"fraction":0.0,"signal":"no OpenAlex id","rationale":null},{"key":"f_metadata_richness","label":"Rich, machine-readable metadata","kind":"llm","weight":1.0,"fraction":0.0,"signal":null,"rationale":"The paper does not provide any machine-readable metadata (e.g., structured data or schema) for the datasets or code; only a human-readable description of data sources is given."}]},"A":{"name":"Accessible","score":55.0,"criteria":[{"key":"a_open_access","label":"Open Access / files deposited","kind":"deterministic","weight":1.5,"fraction":1.0,"signal":"Open Access","rationale":null},{"key":"a_retrievable","label":"Free full text retrievable","kind":"deterministic","weight":1.0,"fraction":0.0,"signal":"0 OA location(s)","rationale":null},{"key":"a_access_protocol","label":"Clear data/code access protocol","kind":"llm","weight":1.0,"fraction":0.5,"signal":null,"rationale":"The paper states that data are available in the Edmond repository with a URL, but does not specify a formal access protocol (e.g., API, authentication, or license) for the code or raw data beyond a generic link."}]},"I":{"name":"Interoperable","score":12.5,"criteria":[{"key":"i_linked_data","label":"Linked datasets / DataCite relations","kind":"deterministic","weight":1.0,"fraction":0.0,"signal":"linked_datasets=0, datacite=0","rationale":null},{"key":"i_standard_ids","label":"References data via standard accessions","kind":"deterministic","weight":1.0,"fraction":0.0,"signal":"accessions=0, trials=0","rationale":null},{"key":"i_standards","label":"Standard formats, vocabularies & identifiers","kind":"llm","weight":1.0,"fraction":0.25,"signal":null,"rationale":"The paper uses standard database names (e.g., Web of Science, Scopus) but does not mention use of standard formats, vocabularies, or persistent identifiers for the data or code (e.g., no mention of DOIs for datasets or standard file formats)."}]},"R":{"name":"Reusable","score":33.33,"criteria":[{"key":"r_license","label":"Clear, open reuse license","kind":"deterministic","weight":1.5,"fraction":0.0,"signal":"no license","rationale":null},{"key":"r_downloads","label":"Demonstrated reuse (downloads)","kind":"deterministic","weight":0.5,"fraction":0.0,"signal":"downloads=0","rationale":null},{"key":"r_version","label":"Versioned / maintained","kind":"deterministic","weight":0.5,"fraction":0.0,"signal":"no version chain","rationale":null},{"key":"r_dataset","label":"Classified as a data resource","kind":"deterministic","weight":0.5,"fraction":1.0,"signal":"is_dataset","rationale":null},{"key":"r_reusability","label":"Data-availability statement, license & reproducibility","kind":"llm","weight":2.0,"fraction":0.5,"signal":null,"rationale":"The paper includes a data availability statement with a repository link, but does not provide a clear license for reuse, nor does it mention code or detailed reproducibility instructions beyond the statistical methods."}]}},"suggestions":["Add a machine-readable metadata file (e.g., JSON-LD or RDF) describing the dataset structure and variables.","Specify a formal access protocol (e.g., API endpoint or license) for the code and raw data, not just a repository URL.","Use standard file formats (e.g., CSV, XML) and include persistent identifiers (e.g., DOIs) for each dataset and code version.","Include a clear open-source license (e.g., CC0 or MIT) for the data and code to enable reuse.","Provide a detailed reproducibility guide or code repository with version control and documentation."],"model":"deepseek/deepseek-v4-flash","agent_version":"fair_agent_v2","fulltext_source":"unpaywall_pdf"},"fair_model":"deepseek/deepseek-v4-flash","fair_agent_version":"fair_agent_v2","fair_fulltext_source":"unpaywall_pdf","fair_has_llm":true,"fair_computed_at":"2026-06-18T00:35:34.835800Z","clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}